Welcome, AimeeH!
Trees BEHIND the dam are no danger to the dam itself. ON the dam, is a bad thing! Roots of a tree underground basically mirror the branches above ground. The outer reach of a tree, called the drip line is how far roots extend also. Those roots will eventually die, and once starting to rot, they leave holes for water to flow through.
If the trees are behind the dam, and the drip line does not extend more than a quarter of the thickness of the dam backside, the only reason to remove them would be for easier equipment maneuvering.
I really like automatic siphon drain systems. You move more water in same size pipes, plus you remove bottom sediments and anoxic water when installed properly.
FWIW, Ponds with Bass and Bluegill need to have bass removed to stay well balanced. Self-Sustaining does not mean quality or fish thriving. A 5 pound Bass is awesome to catch, but in your area, 10+ pounders should be found occasionally.
A pond only supports so many pounds of fish. It is always a dynamic number, but for ease of the explanation, assume the pond supports 1000#. It can be one 1000# fish, one thousand 1# fish, or 16,000 one ounce fish. Self sustaining means fish spawn, and every spawn, you end up with more, but smaller fish in that 1000# example. As pond owners wanting quality, thriving fish, we have to remove 50-100 pounds per surface acre annually in established fisheries to keep them the healthiest.
